Control of Superluminal Light Propagation in a Four-Level Atomic Medium via Laguerre Field Strength and Beam Waist Modulation

<jats:p>We studied and investigated whether light pulses travel faster then light in a four-level atomic medium using a theoretical method. Laguerre-Gaussian (LG) beam waist, denoted by F and strength Z, is regulated in this investigation. We analyses the localized absorption and dispersion properties within the four level atomic medium as well as demonstrate how the group velocity is affected by changing the beam waist. Our results showed that the team index remained negative, with values spanning -0.0015 to -0.0005, and the speed of the group at reduced beam-like waists was among -0.0004 and -0.0002 c. While the superluminal capability remains constant, the level of localized absorption as well as dispersion increases with the pulse waist. This work provides new insights into the flexibility of light propagation on dispersive surfaces, which may be helpful in domains like gravitational wave motion detection methods, soliton scanning systems, and high-frequency optical computation.</jats:p>